There’s no law that requires someone to have a c-card to dive; although it’s certainly "standard practice" in the dive industry. I’m not sure how it affects your safety since you are responsible for your safety and not the other divers. There are lots of divers in the world who have been doing it for decades and predate the scuba "industry" selling c-cards. Usually you find boats that are involved in selling training being the ones who check more for cards.
I wouldn’t expect the boat to have a nitrox tester for you onboard. The fill station probably has one, and if you’re diving nitrox you should have one (and it sounds like you did). The boat may or may not.
Are you sure they tied to the wreck? Most historical wrecks off the FL coast (at least the ones that I’ve dived) have mooring buoys that are maintained by NOAA. The boat would tie off to the buoy. That’s how it has been on every wreck dive I’ve done. The weights and lures sure sound like pollution from people fishing on the wreck to me. I’ve seen that on dives as well. Many fishermen leave a real mess behind. Ever done a cleanup dive? If not, you’d probably be surprised just how much junk there is. If you’re concerned about them taking historical artifacts you can definitely report it. I doubt weights and lures are considered historical artifacts.